Measuring Rates of Reaction for the ESAT

Introduction to Reaction Rates

To understand the kinetics of a chemical system, we must be able to measure how quickly a reaction occurs. The rate of reaction is the speed at which reactants are converted into products. It is usually determined by measuring the change in a specific property of the reaction mixture over time. The choice of measurement method depends on the physical states of the substances involved and the specific chemical properties of the species.

Measuring the Loss of a Reactant

One common method for monitoring a reaction is measuring the decrease in mass of the reaction vessel. This is specifically useful for reactions that produce a gas that is dense enough to escape and result in a measurable change on a balance. For example, consider the reaction between calcium carbonate and hydrochloric acid:

$CaCO_3(s) + 2HCl(aq) \rightarrow CaCl_2(aq) + H_2O(l) + CO_2(g)$

In this setup, the flask is placed on a digital balance. As the reaction progresses, carbon dioxide gas escapes. To ensure accuracy:

1. A cotton wool plug is used in the neck of the flask. This allows the gas to escape but prevents the loss of liquid droplets caused by fizzing, which would otherwise lead to an overestimation of the rate.
2. The mass is recorded at regular intervals, such as every 10 to 30 seconds.
3. The rate is calculated from the decrease in mass over time.

Note that this method is unsuitable for reactions producing hydrogen gas ($H_2$) because hydrogen is so light that the mass change is often within the margin of error for standard laboratory balances.

Measuring the Gain of a Product

If a reaction produces a gas, the volume of that gas can be collected and measured. There are two primary techniques for this:

1. Gas Syringe: The gas produced pushes a plunger out of a calibrated syringe. This is the most precise method as it is unaffected by the density or solubility of the gas.
2. Displacement of Water: The gas is bubbled into an upturned measuring cylinder or burette filled with water. This is suitable for gases with low solubility in water, such as oxygen, but it is incorrect for soluble gases like carbon dioxide or sulfur dioxide, which would dissolve in the water rather than being collected.

Measurement of Physical Properties

When mass or volume changes are not significant, other physical properties can be monitored over time:

1. Colorimetry: If the reaction involves a change in colour, such as the consumption of a brown iodine solution, a colorimeter can measure the change in light absorbance. This provides a quantitative measure of concentration changes.
2. Electrical Conductivity: If the concentration of ions in a solution changes, the conductivity of the solution will change. This is useful for reactions where ionic products are formed from covalent reactants.
3. pH Measurement: For reactions involving acids or bases where the $H^+$ ion concentration changes, a pH probe connected to a data logger can provide a continuous record of the reaction rate.
4. Turbidity (Precipitation): In reactions where a solid precipitate forms from two clear solutions, the rate can be determined by timing how long it takes for the mixture to become opaque. A common example is the reaction between sodium thiosulfate and hydrochloric acid, which produces solid sulfur.

Worked Example: Calculating Rates from Data

In an experiment, $40 \text{ cm}^3$ of hydrogen gas is collected in $80 \text{ seconds}$ during the reaction between magnesium and sulfuric acid. Calculate the average rate of reaction.

$\text{Average Rate} = \frac{\text{Total volume of gas}}{\text{Total time taken}}$

$\text{Average Rate} = \frac{40 \text{ cm}^3}{80 \text{ s}} = 0.5 \text{ cm}^3\text{ s}^{-1}$

In more complex ESAT questions, you may be asked to find the initial rate from a graph. To do this, draw a tangent to the curve at $t = 0$ and calculate its gradient using the formula $\text{Gradient} = \frac{\Delta y}{\Delta x}$.

Selecting the Appropriate Method

Choosing the correct method is a frequent exam requirement. You must consider the state symbols in the equation:

1. If you see $(g)$ as a product, consider gas volume or mass loss.
2. Check the $M_r$ of the gas; if it is very low (like $H_2$), prefer a gas syringe over mass loss.
3. If you see $(aq)$ reactants turning into $(s)$ products, consider turbidity or a change in conductivity.